Statistical Mechanics

by Huang, Kerson

• ISBN13: 9780471815181
• ISBN10: 0471815187
• Edition: 2nd
• Format: Paperback
• Copyright: 1991-01-16
• Publisher: Wiley

Summary

Unlike most other texts on the subject, this clear, concise introduction to the theory of microscopic bodies treats the modern theory of critical phenomena. Provides up-to-date coverage of recent major advances, including a self-contained description of thermodynamics and the classical kinetic theory of gases, interesting applications such as superfluids and the quantum Hall effect, several current research applications, The last three chapters are devoted to the Landau-Wilson approach to critical phenomena. Many new problems and illustrations have been added to this edition.

Author Biography

Kerson Huang is Professor of Physics at the Massachusetts Institute of Technology, Cambridge, USA, and a leading authority on quantum physics. He is a highly experienced textbook writer and has written Statistical Mechanics, also published by Wiley. Professor Huang?s research interests focus on Bose-Einstein condensates and non-renormalizable theories.

Table of Contents

PART A THERMODYNAMICS AND KINETIC THEORY	1	(124)
The Laws of Thermodynamics	3	(28)
Preliminaries	3	(4)
The First Law of Thermodynamics	7	(2)
The Second Law of Thermodynamics	9	(5)
Entroy	14	(5)
Some Immediate Consequences of the Second Law	19	(3)
Thermodynamic Potentials	22	(3)
The Third Law of Thermodynamics	25	(6)
Some Applications of Thermodynamics	31	(21)
Thermodynamic Description of Phase Transitions	31	(4)
Surface Effects in Condensation	35	(3)
Van der Waals Equation of State	38	(5)
Osmotic Pressure	43	(5)
The Limit of Thermodynamics	48	(4)
The Problem of Kinetic Theory	52	(21)
Formulation of the Problem	52	(4)
Binary Collisions	56	(4)
The Boltzmann Transport Equation	60	(2)
The Gibbsian Ensemble	62	(3)
The BBGKY Hierarchy	65	(8)
The Equilibrium state of a Dilute Gas	73	(20)
Boltzmann's H Theorem	73	(2)
The Maxwell-Boltzmann Distribution	75	(4)
The Method of the Most Probable Distribution	79	(6)
Analysis of the H Theorem	85	(5)
The Poincare Cycle	90	(3)
Transport Phenomena	93	(32)
The Mean Free Path	93	(2)
Effusion	95	(1)
The Conservation Laws	96	(4)
The Zero-Order Approximation	100	(4)
The First-Order Approximation	104	(4)
Viscosity	108	(3)
Viscous Hydrodynamics	111	(2)
The Navier-Stokes Equation	113	(4)
Example in Hydrodynamics	117	(8)
PART B STATISTICAL MECHANICS	125	(180)
Classical Statistical Mechanics	127	(16)
The Postulate of Classical Statistical Mechanics	127	(3)
Microcanonical Ensemble	130	(5)
Derivationi of Thermodynamics	135	(1)
Equipartition Theorem	136	(2)
Classical Ideal Gas	138	(2)
Gibbs Paradox	140	(3)
Canonical Ensemble and Grand Canonical Ensemble	143	(28)
Canonical Ensemble	143	(2)
Energy Fluctuations in the Canonical Ensemble	145	(4)
Grand Canonical Ensemble	149	(3)
Density Fluctuations in the Grand Canonical Ensemble	152	(2)
The Chemical Potential	154	(3)
Equivalence of the Canonical Ensemble and the Grand Canonical Ensemble	157	(4)
Behavior of W(N)	161	(2)
The Meaning of the Maxwell Construction	163	(8)
Quantum statistical mechanics	171	(22)
The Postulates of Quantum Statistical Mechanics	171	(3)
Density Matrix	174	(2)
Ensembles in Quantum Statistical Mechanics	176	(2)
The Third Law of Thermodynamics	178	(1)
The Ideal Gases: Microcanonical Ensemble	179	(6)
The Ideal Gases: Grand Canonical Ensemble	185	(4)
Foundations of Statistical Mechanics	189	(4)
General Properties of the Partition Function	193	(20)
The Darwin-Fowler Method	193	(6)
Classical Limit of the Partition Function	199	(7)
Singularities and Phase Transitions	206	(4)
The Lee-Yang Circle Theorem	210	(3)
Approximate Methods	213	(28)
Classical Cluster Expansion	213	(7)
Quantum Cluster Expansion	220	(4)
The Second Virial Coefficient	224	(4)
Variational Principles	228	(2)
Imperfect Gases at Low Temperatures	230	(11)
Fermi Systems	241	(37)
The Equation of State of an Ideal Fermi Gas	241	(6)
The Theory of White Dwarf Stars	247	(6)
Landau Diamagnetism	253	(7)
The De Haas-Van Alphen Effect	260	(1)
The Quantized Hall Effect	261	(6)
Pauli Paramagnetism	267	(5)
Magnetic Properties of an Imperfect Gas	272	(6)
Bose Systems	278	(27)
Photons	278	(5)
Phonons in Solids	283	(3)
Bose-Einnstein Condensation	286	(8)
An Imperfect Bose Gas	294	(4)
The Superfluid Order Parameter	298	(7)
PART C SPECIAL TOPICS IN STATISTICAL MECHANICS	305	(163)
Superfluids	307	(34)
Liquid Helium	307	(4)
Tisza's Two-Fluid Model	311	(2)
The Bose-Einstein Condensate	313	(2)
Landau's Theory	315	(2)
Superfluid Velocity	317	(4)
Superfluid Flow	321	(4)
The Phonon Wave Function	325	(4)
Dilute Bose Gas	329	(12)
The Ising Model	341	(27)
Definition of the Ising Model	341	(3)
Equivalence of the Ising Model to Other Models	344	(4)
Spontaneous Magnetization	348	(4)
The Bragg-Williams Approximation	352	(5)
The Bethe-Peierls Approximation	357	(4)
The One-Dimensional Ising Model	361	(7)
The Onsager Solution	368	(24)
Formulation of the Two-Dimensional Ising Model	368	(6)
Mathematical Digression	374	(4)
The Solution	378	(14)
Critical Phenomena	392	(24)
The Order Parameter	392	(2)
The Correlation Function and the Fluctuation-Dissipation Theorem	394	(2)
Critical Exponents	396	(3)
The Scaling Hypothesis	399	(4)
Scale Invariance	403	(3)
Goldstone Excitations	406	(1)
The Importance of Dimensionality	407	(9)
The Landau Approach	416	(25)
The Landau Free Energy	416	(2)
Mathematical Digression	418	(2)
Derivation in Simple Models	420	(2)
Mean-Field Theory	422	(4)
The Van der Waals Equation of State	426	(2)
The Tricritical Point	428	(6)
The Gaussian Model	434	(3)
The Ginzburg Criterion	437	(1)
Anomalous Dimensions	438	(3)
Renoremalization Group	441	(27)
Block Spins	441	(2)
The One-Dimensional Ising Model	443	(3)
Renormalization-Group Transformation	446	(3)
Fixed Points and Scaling Fields	449	(3)
Momentum-Space Formulation	452	(3)
The Gaussian Model	455	(3)
The Landau-Wilson Model	458	(10)
APPENDIX N-BODY SYSTEM OF IDENTICAL PARTICLES	468	(19)
A.1 The Two Kinds of Statistics	468	(2)
A.2 N-Body Wave Functions	470	(7)
A.3 Method of Quantized Fields	477	(7)
A.4 Longitudinal Sum Rules	484	(3)
Index	487